We prove that, for m greater than 3 and k greater than m - 2, the Grassmannian of m-dimensional subspaces of the space of skew-symmetric forms over a vector space of dimension 2k is birational to the Hilbert scheme of Palatini scrolls in P(2k-1). For m = 3 and k > 3, this Grassmannian is proved to be birational to the set of pairs (epsilon, Y), where Y is a smooth plane curve of degree k and epsilon is a stable rank-2 bundle on Y whose determinant is O(Y) (k - 1).
Skew-symmetric matrices and Palatini scrolls
FANIA, Maria Lucia
2010-01-01
Abstract
We prove that, for m greater than 3 and k greater than m - 2, the Grassmannian of m-dimensional subspaces of the space of skew-symmetric forms over a vector space of dimension 2k is birational to the Hilbert scheme of Palatini scrolls in P(2k-1). For m = 3 and k > 3, this Grassmannian is proved to be birational to the set of pairs (epsilon, Y), where Y is a smooth plane curve of degree k and epsilon is a stable rank-2 bundle on Y whose determinant is O(Y) (k - 1).File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
